Analyzing the sophistication of Chinese checkers
Introduction
The game refinement (GR) theory has been proposed earlier by Iida et al. [1] to determine the level of sophistication of games. It had been utilized as a tool to measure the sophistication of board games, sports games, and video games [2], [3], [4], [5]. The GR theory had provided an essential understanding of relationships between the elements of skill and chance of eventual convergence towards . Also, many facts have been revealed regarding temporal changes in the attractiveness of the evolution of games [1], [6]. However, the GR theory is yet to shed some light on other relevant research areas such as multiplayer games. Chinese checkers is one such game.
Chinese checkers is a strategy board game which can be played by up to six people, playing individually or with partners. The game is a modern and simplified variant of the American game Halma [7]. The game objective is to be the first to race all of one’s pieces across the hexagram-shaped board into “home”, the corner of the star opposite one is starting corner using single-step moves or moves that jump over other pieces. Chinese checkers has multiple variants, depending on the board shapes and sizes. The mainstream Chinese checkers are the hexagonal board, which can be played by up to six people, and each player controls ten pieces on the board.
Thus, this study focuses on analyzing the game entertainment through the performance level of the player, the number of players, and the board sizes. Moreover, the simulation of Halma is also conducted to observe its historical development into the modern Chinese checkers. As such, this study attempts to answer the following questions:
- 1.
What is the most comfortable number of players in Chinese checkers?
- 2.
What is the link between performance level and entertainment?
- 3.
What regulations (board size in this case) are more entertaining?
This research quantified the entertainment values of the Chinese checkers game using the GR theory in several simulation games to address such questions. The game simulation was realized by implementing AI to self-play the game. Since the GR measure is the point gained by the players, the mathematical model of the GR theory will be applied to this game, and the refinement values will be calculated to determine the most suitable number of players. The impact of different board settings to the game experience was also investigated.
This paper is organized as follows. Section 2 introduces the related work about multiplayer games and Chinese checkers. In Section 3, an overview of the Chinese checkers and its implementation are given. Then, the fundamental idea of GR theory and the experimental setups were given in Section 4. Then, the obtained results were analyzed and discussed in the Section 5. Finally, Section 6 conclude this paper.
Section snippets
Multiplayer games
Multiplayer game is one of the popular research focus in the game domains. A multiplayer game is a game which is played by more than two players. The players might be independent opponents, formed into teams, or be just a single team pitted against the game. Many works in the multiplayer games have been published, such as different approaches to the development of the multiplayer algorithms and its comparison [8], [9], multiplayer Go [10], decision algorithms for multiplayer non-cooperative
Chinese checkers
Chinese checkers is a modern and simplified variant of the American game Halma. Halma is a strategy board game invented in 1883 by George Howard Monks, a US thoracic surgeon at Harvard Medical School. The game board is checkered and divided into 8 × 8, 10 × 10, or 16 × 16 squares board, either of which is adequate for two players and they have 10, 15 and 19 pieces per player, respectively. The game is won by being first to transfer all of one’s pieces from one’s camp into the camp in the
Analysis of Chinese checkers using game refinement theory
In the experiments, we set four battle modes, which are two, three, four, or six players, respectively. Meanwhile, to observe the historical development of the Chinese checkers, the simulation was also conducted on the ancestor of Chinese checkers: Halma. The battle modes were realized by self-play AI simulation. Five players’ mode was excluded to avoid the unfairness of board space. This situation is considered because it would afford one player, the one with no opponent across from him, to
Discussion
The experiment conducted on the different player numbers found that three players mode has the highest refinement value () among these four battle modes, which is closest to the most appropriate region of the GR theory. Thus, it is reasonable to infer that three players mode in Chinese checkers provides the players with the highest enjoyment. Also, the initial experiment on Halma game found that the GR measure of Halma is far below the appropriate range (), even when compared to
Conclusion
The GR theory has been applied to measure the entertainment and sophistication of the board games, video games, and sports. In this study, we extended this theory to a multiplayer game, Chinese checkers. It was found that the evolution of Chinese checkers is reasonable because the game improves towards more exciting and attractive settings, but not sophisticated enough with the development of history. Also, the recommended number of players to play Chinese checkers is three people. In the three
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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